Question

Let f(x) be the piecewise function defined above. Which of the following statements is false?

A) f(x) is continuous at x=1
B) f(x) is not defined at x=2
C) f(x) is continuous at x=3
D) f(x) is continuous on the entire domain

Answer 1

The question asks which of the following statements is false regarding the piecewise function f(x). The false statement is that f(x) is continuous on the entire domain. The correct option is D.

Step-by-step explanation:

The question asks which of the following statements is false regarding the piecewise function f(x). Let's analyze each statement:

A) f(x) is continuous at x=1: This statement is true because f(x) is continuous at x=1 since the function values from both sides of x=1 approach the same value.

B) f(x) is not defined at x=2: This statement is true because f(x) is not defined at x=2 as there is a discontinuity or a hole at that point.

C) f(x) is continuous at x=3: This statement is true because f(x) is continuous at x=3 as the function values from both sides of x=3 approach the same value.

D) f(x) is continuous on the entire domain: This statement is false because we know that f(x) is not defined at x=2, so it is not continuous on the entire domain.

Therefore, the correct answer is D) f(x) is continuous on the entire domain is false.